In general, systems of the prior art for controlling the dyeing of a moving web operate by measuring the tristimulus values X, Y and Z of light reflected from a moving portion of the web. The tristimulus values, which are roughly equivalent to the "red," "green" and "blue" components, respectively, of the reflected light, are either measured simultaneously by different detectors, as in De Remigis U.S. Pat. No. 3,936,189, or successively using a filter wheel or the like as in Lodzinski U.S. Pat. No. 4,019,819. The tristimulus values X, Y and Z are either used directly for control purposes or are first converted to other coordinates such as Hunter coordinates L, a and b.
While three- or four-filter colorimeters of the type described above are common in the art and are adequate for ordinary control applications, they suffer serious drawbacks. First, the X, Y and Z tristimulus outputs are only indicative of the perceived color of the web under the illuminant used in the colorimeter. A color "match" obtained in terms of tristimulus values using a standard illuminant does not necessarily indicate a match with an illuminant having a different spectral composition, and, in general, it is impossible to predict the color properties of a material with a given illuminant if only its tristimulus values X, Y and Z are known. Further, if the actual spectral curves of the illuminant or detector used in the colorimeter differ from those for which the filters were designed, the tristimulus values obtained will not necessarily even indicate the color properties of the material under a standard illuminant. While Lodzinski does suggest, as an alternative, using a relatively large number of narrow-band filters so as to approximate an abridged spectrophotometer, he suggests no practical implementation of this proposal in an on-line system.
Another defect of control systems of the prior art arises from the nonlinearity of the relationship between the tristimulus values X, Y and Z and the dye concentrations to be controlled. While this nonlinearity is relatively insignificant at low dye concentrations, it increases with dye concentration so that, when relatively saturated colors are being sought, the nonlinearity is substantial. As a result, in practical systems, the relationship between X, Y and Z and the dye concentrations must be linearized about some nominal setpoint to make the computation tractable. This need for linearization is obviously disadvantageous, since not only does the operating point vary about the setpoint, but the setpoint itself is often changed, necessitating a recomputation of the linearized equation.
McCarty U.S. Pat. No. 3,601,589 discloses a system for selecting pigments to match a given surface coating in which an initial pigment formulation is generated in advance of actual mixing by selecting those concentrations which minimize the total square error between the measured reflectance of the coating being matched and the computed reflectance of the pigment formulation. However, the actual mixing process itself is controlled by sampling the mixture with a colorimeter and using L, a and b coordinates computed from the colorimeter output to correct the initial pigment formulation.